Flame Speed Measurements

Transcription

1 Mle Fractin Temperature (K) Premixed Flames: Flame Stretch and 0.2 Flame Speed Measurements Jerry Seitzman and Ben Wilde CH4 H2O HCO x 1000 Temperature Methane Flame Distance (cm) FlameStretchSpeedMeasure -1 Idealized Premixed Flame Simplest pssible premixed flame cnfiguratin 1-dimensinal, planar adiabatic T b =T ad Adiabatic Flame Temperature ρ u u u =ρ u S =ρ b u b Mass Burning Flux What are the cntrlling parameters? thermal and mass diffusivities reactin rates temperature f reactants pressure exthermicity f fuel/xidizer S Fundamental prperty f fuel/xidizer mixture FlameStretchSpeedMeasure -2 1

2 Nn-Ideal Premixed Flames Nn-adiabatic 3-dimensinal Nn-unifrm and/r unsteady flw In general, S u S Mass burning flux ρ u S Rendering f1200k istherm frm DNS f a turbulent Φ=0.37 H2 flame clred by lcal H 2 cnsumptin rate, Reactants Day et al. Cmbustin and Flame (2009) FlameStretchSpeedMeasure -3 Stretched Flames: Basics Flames subject t aerdynamic nn-unifrmity and/r unsteady effects are called Stretched Flames Flames can be distrted, wrinkled r displaced by nnunifrm r unsteady flw fields - called Hydrdynamic Stretch Stretched flames respnd t nn-unifrm r unsteady flw fields they encunter by mdificatin f the temperature and/r species prfiles in the diffusive zne, changing flame prpagatin rate - called Flame Stretch Hydrdynamic stretch and flame stretch are inherently cupled cncepts! FlameStretchSpeedMeasure -4 2

3 Stretched Flames: Physical Perspective Stretch causes a misalignment between cnvective and diffusive fluxes near the flame Stretched flames are nt infinitely thin (therwise kinematic restratin wuld dminate) Stretch effects help t explain a wide variety f interesting and imprtant physics nt bserved in premixed 1D, planar, adiabatic laminar flames: Flame speed Flame shape Flame stability S m S 0 1 D, planar, adiabatic m FlameStretchSpeedMeasure -5 Tips f Bunsen Flames Prpane (heavier than air) and methane (lighter) Prpane(C 3 H 8 ) Methane(CH 4 ) d=10mm = ref: Mizmt, Asaka, Ikai and aw, Prc. Cmbust. Inst. 20, 1933 (1984) FlameStretchSpeedMeasure -6 3

4 Tip Opening Prpane flames f increasing richness Prpane(C 3 H 8 ) Methane(CH 4 ) = ref: Mizmt, Asaka, Ikai and aw, Prc. Cmbust. Inst. 20, 1933 (1984) FlameStretchSpeedMeasure -7 Bunsen Tip Flame Temperature Data CH 4 -air Curvature/stretch can cause enhancement r reductin in flame temperature cmparisn f measured T tip t T ad CH 4 vs. C 2 H 4 vs. C 3 H 8 C 3 H 8 -air T ad T meas ref: C.K. aw, Cmbustin Physics C 2 H 4 -air FlameStretchSpeedMeasure -8 4

5 Stretched Flames: Gemetry Stretch effects exist because f cupling between flame surfaces and flw fields Real flames are 3-D unsteady deflagratin waves Assuming the flame is thin, smth and cntinuus we can treat the flame as a 3-D surface Burned n n n n n x, t Unburned FlameStretchSpeedMeasure -9 Flame Stretch Rate Definitin Cnsider simple case f prpagating flame Flame stretch rate can be defined as nrmalized rate f change f flame surface area element 1 da Williams (1975) A dt agrangian quantity units f flame stretch are 1/s, i.e. an inverse time scale Burned da Unburned FlameStretchSpeedMeasure -10 5

6 Influence f Flame Stretch Tw basic cases psitive stretch (flame in tensin) negative stretch (flame in cmpressin) P P 1 da A dt R R R related t strain, curvature,dilatatin P P like Bunsen tip thermal diffusin () fcuses int reactants, enhances S (same fr mass diffusin f radicals) mass diffusin f reactants away frm centerline, can R reduce [reactants], reactin rate and thus S differential diffusin can lead t less stichimetric mixture, greater diffusinal lss f deficient reactant, reduces S e=1, ppsing effects tend t cancel FlameStretchSpeedMeasure -11 P Stretched Flames: Gemetry Flame surface mves, defrms, and accelerates/decelerates, as a functin f space and time FlameStretchSpeedMeasure -12 6

7 FlameStretchSpeedMeasure -13 Sign Cnventins κ Nrmalized time rate f change f flame surface area Given previus sign cnventin fr stretch rate can interpret based n directin frm which heat flux vectrs crss the sidewalls f a differential cntrl vlume immediately adjacent t flame sheet Heat flux int the sides f the cntrl vlume negative stretch rate Heat flux ut f the sides f the cntrl vlume psitive stretch rate 1 da A dt Curved flame in unifrm velcity flw Flat flame in diverging flw Flame Surface Prpagatin G Eqn. evel set apprach arises very naturally fr the purpse f defining the flame surface in thin, smth, and cntinuus premixed flames Describe the surface f the flame as, Gx, t 0 Set G>0 in prducts and G<0 in reactants At flame G n G dg G F G 0 dt t FlameStretchSpeedMeasure -14 7

8 Stretched Flame Analysis Full expressin in terms f flame surface variables, ut1 ut2 ( vf n)( n) t ut ( vf n)( n) t t 1 2 κ a -stretch due t tangential velcity gradients at the flame surface κ b -stretch due t unsteady flame curvature 1 T S u u 2 n nx, t u s n v u Alternative expressin, u u nn : u u s ( n) n S n u s ( n) S curv κ S -stretch due t flw nn-unifrmities κ curv -stretch due t a curved flame in a unifrm apprach flw a b F FlameStretchSpeedMeasure -15 Stretched Flame Analysis If we cnsider statinary flames, v 0 u n nu F since t u n u n t t FlameStretchSpeedMeasure -16 8

9 e Effects n Stretched Flames Each reactant has different D ij (multi-cmpnent mixture) mst deficient reactant and/r reactant with largest gradient is generally the cntrlling parameter fuel if lean, xygen if rich Three diffusivities f interest: thermal diffusivity, α e Nn unity deficient reactant diffusivity, D i ei, e j Di D abundant reactant diffusivity, D j Tw effects arise because f differences in diffusivities nn-unity e: imbalance between thermal and mass diffusivity differential diffusin: imbalance between deficient and abundant species diffusivities D j FlameStretchSpeedMeasure -17 Nn-Equidiffusive Effects Flame respnse t stretch effects is strngest in flames with ewis numbers much different frm ne Flame respnse in stretched flames depends n the sign f the stretch rate and the ewis number fr fixed premixed mixture, flame respnse will change entirely when stretch rate changes sign frm psitive t negative fr fixed stretch rate, flame respnse will change entirely when e transitins frm greater than t less than a critical value (e crit =1 fr flame temperature) Thery predicts and experiments cnfirm that equidiffusive stretched flames are insensitive t the magnitude f stretch FlameStretchSpeedMeasure -18 9

10 Stretch Effects in Bunsen Flames Statinary, axisymmetric flame Curved flame with negative stretch Assume unifrm velcity prfile exiting the tube Diffusive fluxes d nt align with cnvective fluxes Fr negative stretch case if thermal cnductin utweighs mass diffusin then flame speed enhanced ( vs. D) s S fr e > 1 similarly S fr e < 1 P R P FlameStretchSpeedMeasure -19 Nn-unity e and Negative Stretch Cnsider Bunsen flames tip f flame=negative stretch R Fuel lighter than air (e.g., CH 4 ) MW fuel < MW mix fr <1, e deficient = mix /D fuel drps as S fr leaner mixtures tip weak (pen) fr sufficently lean flames enhanced fr rich flames Methane(CH 4 ) 1.52 FlameStretchSpeedMeasure P 10

11 Nn-unity e and Flame Stretch Fr fuel heavier than air (e.g., C 3 H 8 ) MW fuel > MW mix e deficient as S fr lean mixtures tip enhanced fr sufficiently lean flames tip weak (pen) fr rich flames Prpane(C 3 H 8 ) FlameStretchSpeedMeasure -21 R P Tip Opening Prpane flames, richer=mre stretch sensitivity Prpane(C 3 H 8 ) Methane(CH 4 ) = max stretch lcatin ref: Mizmt, Asaka, Ikai and aw, Prc. Cmbust. Inst. 20, 1933 (1984) FlameStretchSpeedMeasure

12 Stretch Effects: Oppsed Flw Flames Flw induced stretch example: stagnatin flame (psitively stretched) diffusin nt aligned with flw Examples premixed reactants impinging n a flat wall premixed reactant impinging n ht prducts FlameStretchSpeedMeasure -23 Stretch Effects: Unsteady Spherical Flames Stretch rate changes as a functin f radius Curvature is present but flw velcities align with flame surface nrmal Statinary spherical flame wuld be stretchless ut1 ut2 ( vf n)( n) t ut ( vf n)( n) t t 1 2 a b Cmbustin Physics by C.K. aw (Cambridge University Press, 2006) FlameStretchSpeedMeasure

13 Stretched Flames: e1 Φ=0.27 Φ=0.27 Φ=0.37 T u =298K P=1atm e>1 FlameStretchSpeedMeasure -25 e 1 e<1 Bell et al. Prceedings f the Cmbustin Institute (2007) Flame Speed Crrectins S fr stretched flames, need t mdify 1d flame speed t accunt fr curvature, flw divergence Fr small perturbatins (lw amunts f stretch), asympttic analysis (Markstein) leads t the fllwing fr the apparent flame speed S S Markstein ength S Ma Smetimes expressed in terms f Karlvitz number residence time fr crssing unstretched flame f S f Ka characteristic time fr flame stretching 1 S S S MaKaS f Markstein number Ma f S S 1 MaKa FlameStretchSpeedMeasure

14 S S? 1 Karlvitz Dependence MaKa Flame speeds fr prpane-air mixtures fr different Ka Ma=Ma() 2 S S 1 FlameStretchSpeedMeasure Ka after Tseng et al., Cmbust. and Flame 95, 410 (1993) Saw befre Ma=Ma() Markstein Number Try simple linear crrelatin Ma=S( n ) 4 Ma Air/ S n Ka max 2 Fuel C 3 H S S 1 MaKa Prpane-Air 1 atm C 2 H C 2 H H CH FlameStretchSpeedMeasure Crrelatin Ma = 8.8(-1.44) after Tseng et al., Cmbust. and Flame 95, 410 (1993) n

15 Flame Speed Measurements Measurements f S are difficult hard t achieve adabatic and 1-d cnditins usually cmprmise and try t crrect Varius methds Bunsen-type burners ( simplest ) traveling tube spherical bmbs sap bubbles flat flame burners stagnatin flames FlameStretchSpeedMeasure -29 Bunsen (Tube) Burner Methd Premixed fuel/air in cylindrical tube laminar varius velcity prfiles statinary flame when nrmal cmpnent f lcal apprach velcity=s uter flame S (nnpremixed) FlameStretchSpeedMeasure -30 u n u ref: Sébastien Ducruix inner cne clr schlieren CH 4 /air =

16 Bunsen (Tube) Burner Methd Appraches measure, u (r u n ) u n u nt necessarily same as u exit u, may nt be cnstant (depends n exit prfile) measure flame area m ua S m exit u Aflame hw t identify flame surface FlameStretchSpeedMeasure -31 schlieren, shadw, luminsity, S u luminusity particle tracks <1 ref: Echekki and Mungal, Phys. Fluids A 2, 1523 ( 1990) Bunsen Methd: Flame Surface Flame surface measurement luminus, schlieren, shadw give different A flame Shadw clsest t Visible Q unburned regin but nt 1-d flame stretch effects Schlieren Shadwgraph S S uminsity crrespnds t high T rxn zne ref: Ibarreta and Sung, 3 rd Jint US Sectin Meeting Cmb. Instit. FlameStretchSpeedMeasure

17 Bunsen Methd: Burned Surface Area Measure reactin zne area (A b ) frm flame luminsity Unstretched laminar flame speed (S ) bsb bsb m Ab m u Q S A A u u u b b flame curvature effect is small fr S b flame strain primarily restricted t tip FlameStretchSpeedMeasure -33 use tall flames CH 4 /C 3 H 8 ~ 80:20 (vl.) H 2 O/Air ~ 19% (mass) 5 atm, 650 K F ~ mm Chemiluminescence image ref: Kchar, Seitzman FlameStretchSpeedMeasure -34 Prpagating Methds Transparent Tube fill tube with premix gases, ignite, watch flame prpagate (make sure it is sustained prpagatin) gas mves ahead f flame frnt (cmpressed) u f > S, and gases may be slightly preheated nn-1d (bundary layer), buyancy dr f Spherical Bmb u f fill clsed spherical chamber, dt watch flame prpagate R f unburned velcity (and p,t u?) cntinuusly increasing nt 1-d (planar), affected by curvature and strain, must extraplate back t zer stretch u f u r 17

18 Axial velcity (m/s) Flat Flame Burner Cnstruct unifrm velcity prfile using prus plate, sintered metals, r small flw passages Burner is either water cled r naturally cled Flame can be essentially S flat except at edges f burner Measurement f flame Q velcity easy (u exit ) Nnadiabatic measure cling, extraplate t Q=0 r T prfile and cmpare with cmputatin; kay fr lw pressures ref: Glassman FlameStretchSpeedMeasure -35 Stagnatin Flames Oppsed jets r jet and stagnatin plate Nzzle Stagnatin plug Stagnatin plug Nzzle 2 Stagnatin plane Flame Nearly flat flames (n curvature), but with aerdynamic strain due t deceleratin caused by stagnatin plane extraplate t zer-strain t btain S FlameStretchSpeedMeasure ref: J. Natarajan PhD thesis Plug Su Flame X 0.4 K=-du/dx D U Nzzle Distance frm stagnatin plane X (mm) 18